State tax filing

In regards to your first question, you would want to prepare your nonresident return for MO first.  This would allow you to claim a Credit for taxes paid to another state on your resident IL return. 

If you are concerned, go back into the state interview section of the program.

1. Go over your MO interview section again. 
2. Then go over your IL interview section again to ensure it pulls in the credit for the taxes paid on your MO return.

In regards to your credit for St. Louis, you can enter that into the Illinois state interview section.

1. Proceed through the screens until you see Take a look at Illinois credits and taxes
2. Select Credit for taxes paid to another state
3. When you see the following screen, select Add Another State

You will see the following screen.  Be sure to put the state as MO, but select the box for City, County, or Locality taxes.  Then enter the amount of your St. Louis city taxes in this section.